Why do we even have that lever?

It's part of a qualification/training complex! The original owners wanted the graduates of the training program to all meet a minimum standard of speed and agility at the end.
When not in use, a heavy object is placed on the button so people can get through.

Why is the only access to many doors, including some bedrooms and the like, in this place parkour?

 

The dungeon used to be part of a were-bat commune, the doors are supposed to be accessed via flying and those protruding stones and wooden poles were perching stands.
Why is there a Sphere of Annihilation in that decorated hole in the wall that looks like a door?

 

Game answer: garbage disposal.

Real answer: Tomb of Horrors is an exception to this game, because it's actually, in-fiction, one big piece of schmuck bait designed to lure in and kill adventurers so the demilich could harvest their souls.

Snarky answer: You missed the best traps in ToH to do this with:


Acererak had some wild parties.

Anyway.

Why do you have to play a song on a giant piano to open the door to this room?

 

It was a party game! The hosts would set up a song and the guests would havw to figure out which one to get in.

Why do mashy spike plates try to mash you in this corridor?

 

You're in the old cidery. This area is famous for its apples, and this building held facilities to mash fruit for cider manufacturing.

Why is this tower only accessible by swimming across a lake of lava?

 

The tower holds a laboratory with exacting cleanliness standards; the scientists, being dragonfolk, could swim through without being harmed and simultaneously have any outside contaminents burnt off.

 

It was an exclusive venue for dragons and salamanders back in its day-- invite only, with very good food and drinks. Swimming across the lake of lava was both a way to prove that you belonged with the in club and a way to get the partygoers in the mood for some fun.

Why is this bottomless pit only scalable if you smash the pillars into bridges?

 

(Yeah, I tried to find one that could have another explanation than "Obvious schmuck bait", it's... Pretty hard.)

There used to be rope bridges that rotted off because of the humidity. You could actually see the points at which the ropes attached to the pillars, that is, until you smashed them, you jerk.
Why is there so much flowing lava in here?

 

it was an easy way to add a light source, and public garbage disposals. And the owners were really stingy with their torch budget, so the builders had to figure something out.

[Edit:] Why does the room fill with poison gas when I grab the glowing ball in the center of the room?

 

trap please?

 

This was originally the site of a temple to a volcano god, and where better to build such a temple than near a volcano? This room opens onto a volcanic vent, the better to hear the Holy Word. The 'glowing ball' was the power source of an air filtration system and now you're getting a lungful of hydrogen sulfide.

Why do these doors teleport me to another room, rather than letting me into the adjacent rooms?

 

That building was last used as an extremely packed housing unit. Forgoing hallways in favor of teleportation lets you fit way more people into the same space without further cramping their quarters or violating privacy by making everyone walk through their neighbors' rooms to get around.

Why is the power source to open this door stored in unattached spheres found lying around in rooms that don't even use their electricity?

 

It's unsafe to keep them plugged in for too long, as they could discharge too much and cause a fire or something. They're supposed to be stored in a crate right next to the door, but someone just kept doing the autopilot error "I stuck the TV remote in the fridge again" thing.

Why do you need to win a riddle contest against a disembodied voice to open this door?

 

Well See, they Used to be in that shelf in the room but unfortunately, the formers owners had a cat.

Why does one lever open the door to the secret lab, but the other dump you into a lake full of crocodiles?

 

The east wing was used to house amphibious peoples from a neighboring kingdom in as a way to promote good diplomatic relations, and there needed to be high levels of humidity to keep their skin moist and the people healthy. However the humidifying systems have broken down in the years since the abandonment of the complex and overproduced, creating fog.

The lab was originally for studying ecology and the lake was a sampling ground. The crocodile numbers have skyrocketed in recent years due to food abundance.

Why do you have to use the same four stones to open each door, but the doors close when those stones are removed only allowing one door to be open at a time?

 

The facility originally studied infectious disease - the doors functioned as airlocks to keep any possible contamination or breach of control contained.

Why do bolts of lightning occasionally shoot down from the ceiling?

 

It was a thesis project on renewable energy sources - originally, there was a mechanism to charge electrical appliances and batteries with the generator that ran on the power from the lightning strikes. But there's easier, safer ways to get power - ones that don't induce staticky hair. So it got shelved and the components (like the generator) got reused for other things. But the mechanism that creates the lightning is still functional, and the occasional lightning bolts are a result of it attempting to safely discharge the build-up of energy that's resulted.

Why are there tanks full of carnivorous fish right under the narrow/fragile walkways through this room?

 

You're in the ornamental aquarium, on the walkway to allow aquarium technicians to feed the fish. It used to have handrails, but they were gilded and scavengers stole them for the valuable metal after the place was abandoned.

Why do jets of lava shoot out of the floor at periodic intervals?

 

It's an art piece! There's supposed to be a shield around each of the jets so you cannot walk into it but someone stole it.

Why do you have to gather keys from a maze made entirely of spikes to open this door?